Yes, priming a wine will work and if you haven't stabilised there will always be a few yeasties which will take an interest in the extra bit of sugar you've added.
But, don't overdo it, aim for a gentle spritz and not a fizz. You will get a light bottle sediment and it won't compact like a bottle conditioned beer, so there's a good chance it will get stirred up when you open the bottle.
Above all, use sparkling wine or proper champagne bottles. Plastic bottles (e.g. 500ml cola or litre spirit mixers) will work too if you're not bothered about aesthetics.
If you want clear, fizzy wine you've got do the champenoise bit with upside-down bottles, freezing the sediment in the neck of the bottle, followed by disgorgement. Either that or force carbonate.